Best Known (86−26, 86, s)-Nets in Base 5
(86−26, 86, 262)-Net over F5 — Constructive and digital
Digital (60, 86, 262)-net over F5, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 10)-net over F5, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 1 and N(F) ≥ 10, using
- net from sequence [i] based on digital (1, 9)-sequence over F5, using
- digital (46, 72, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 36, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 36, 126)-net over F25, using
- digital (1, 14, 10)-net over F5, using
(86−26, 86, 673)-Net over F5 — Digital
Digital (60, 86, 673)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(586, 673, F5, 26) (dual of [673, 587, 27]-code), using
- 43 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0) [i] based on linear OA(581, 625, F5, 26) (dual of [625, 544, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 43 step Varšamov–Edel lengthening with (ri) = (2, 0, 1, 5 times 0, 1, 12 times 0, 1, 21 times 0) [i] based on linear OA(581, 625, F5, 26) (dual of [625, 544, 27]-code), using
(86−26, 86, 59598)-Net in Base 5 — Upper bound on s
There is no (60, 86, 59599)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 1 292654 180420 640387 761402 648109 037548 826662 794449 824486 070029 > 586 [i]